Question

[asy] size(9cm); draw((-1.15,0)--(0.15,0),Arrows); draw((0,0.03)--(0,-0.03)); draw((-1,0.03)--(-1,-0.03)); for(real i=-0.9; i<-0.05; i+=0.1){ draw((i,0.02)--(i,-0.02)); }; label("$-1$",(-1,-0.02),S); label("0",(0,-0.02),S); label("$\spadesuit$",(-0.4,-0.01),S); [/asy] What is the simplest fraction whose value is equal to the number $\spadesuit$ depicted on this number line?

Answer 1

To determine the value of the number $\spadesuit$ depicted on the number line and find the simplest fraction equivalent to it, we need to analyze the position of $\spadesuit$ in relation to the tick marks on the line.

Looking at the number line, we see that $\spadesuit$ is located between $-0.4$ and $-0.3$. To express this as a fraction, we can consider it as the midpoint between these two values. The midpoint can be calculated as the average of $-0.4$ and $-0.3$, which is $-0.35$.

Now, to express $-0.35$ as a fraction in simplest form, we write it as $\frac{-35}{100}$. Simplifying the fraction by dividing the numerator and denominator by their greatest common divisor, which is $5$, we get $\frac{-7}{20}$.

So, the simplest fraction whose value is equal to the number $\spadesuit$ depicted on the number line is $\frac{-7}{20}$.

In summary, by identifying the position of $\spadesuit$ on the number line, determining it as the midpoint between $-0.4$ and $-0.3$, and expressing this midpoint as a fraction in simplest form, we find that $\frac{-7}{20}$ represents the value of $\spadesuit$ on the given number line.